The present invention relates to a system and method for target identification using a Bayes optimal estimation approach.
It is often desirable that sensing systems be able to exploit the data they collect for interesting and relevant information. A task that often falls on human analysts is the examination of sensor data for targets (e.g. vehicles, buildings, people) of interest and the labeling of such objects in a manner aligned with the collection objective (e.g. friend/foe, seen before/new, authorized/unauthorized, etc.). Target detection and identification is a fundamental problem in many applications, such as in hyperspectral imaging, computer-aided diagnosis, geophysics, Raman spectroscopy and flying object identification. Under limited conditions, this task has been automated by machine learning algorithms. Such algorithms are typically trained with examples drawn from the sensor data they are meant to later process autonomously.
The problem is fundamentally one of crafting a decision rule R: → that maps evidence (Eε) to some element of the set of hypotheses (),                Hi: E arises from Ti (target i)        Ho: E does not sufficiently support any targetDecision methods that provide a minimum decision error rate require knowledge of the posterior distribution of target type (p(T|E)).        
In many instances, the physical situation from which the problem arises is expressed in a state variable representation. The internal state variables are the smallest possible subset of system variables that can represent the entire state of the system at any given time. The state variable representation can be expressed asst=A(t)s+W 
Where s is the vector of state variables,                st is the time derivative of s,        A(t) is the state transition matrix, and        W is a noise vector.        
Some of the states can be related to measurements while other states are not related to measurements due to sensor limitations, excessive noise and other factors. The states that are not related to the measurements are often referred to as “hidden variables” or “hidden states.”
It is generally the case that the dimensionality of  is high and so a common approach is to use expert knowledge of the system to develop a projection to a lower dimensional measurement space h: →1×2 . . . ×F, where we presume F distinct measurement variates made from E. This approach has the distinct advantage of reducing training sample sparsity and allowing the designer to exploit ‘features’ with desirable properties known a-priori. This approach has the unfortunate consequence of complicating the calculation of p(T|E). In particular, unless properly conditioned, the measurement variates are correlated and may not be simply combined.
In many cases, the hidden states are replaced by estimated values.
There is a need for a target estimator that properly conditions measurement variates in the case of a series of sensor measurements collected against a target.
There is also a need for a system model that captures visible and hidden stochastic information including, but not limited to target state, target identity, and sensor measurements.
There is a further need for a dynamic mixed quadrature expression facilitating real-time implementation of the estimator.